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Europhysics Letters (EPL)

Spectral properties of two-dimensional Hubbard model with anisotropic hopping

V. Zlatić, P. Entel, S Grabowski

Published Jun 20, 1996• 10 citations
Publisher

Abstract

The zero-temperature spectral properties and Fermi surface (FS) anomalies of hole-doped 2D Hubbard model with anisotropic nearest-neighbor hopping are evaluated using the perturbation theory. The nested sections of the FS, which are always present in the anisotropic model, are found to expand with the strength of Coulomb correlation U. The renormalized FS and the low-energy part of the density of states obtained for small anisotropy and large U are similar to those obtained for large anisotropy and small U. The effect of correlation at low doping can best be described as an enhancement of the hopping anisotropy. The anomalous spectral features are mainly due to the van Hove singularities, which give rise to the momentum dependence of the self-energy.

DOI
10.1209/epl/i1996-00516-1

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The zero-temperature spectral properties and Fermi surface (FS) anomalies of hole-doped 2D Hubbard model with anisotropic nearest-neighbor hopping are evaluated using the perturbation theory. The nested sections of the FS, which are always present in the anisotropic model, are found to expand with the strength of Coulomb correlation U. The renormalized FS and the low-energy part of the density of states obtained for small anisotropy and large U are similar to those obtained for large anisotropy and small U. The effect of correlation at low doping can best be described as an enhancement of the hopping anisotropy. The anomalous spectral features are mainly due to the van Hove singularities, which give rise to the momentum dependence of the self-energy.
The self-energy of the hole-doped two-dimensional (2D) Hubbard model is calculated to second order in the interaction U and the ensuing renormalization of the spectral properties and of the Fermi surface is discussed. In uncorrelated systems the square-shaped Fermi surface separates the Fermi surface closed around the \ensuremath{\Gamma} point (with more holes than particles) from the Fermi surface closed around the Z point (with more particles than holes). In a correlated system a topological change from a Fermi surface centered around the \ensuremath{\Gamma} point to a Fermi surface closed around a Z point is induced, either by increasing the interaction or by diminishing the concentration of holes. The shape of the renormalized spectral function Ap{\mathit{A}}_{\mathbf{p}}Ap​(\ensuremath{\omega}) is momentum dependent. Using Ap{\mathit{A}}_{\mathbf{p}}Ap​(\ensuremath{\omega}) we evaluate dispersion of single-particle excitations. At low energies the band of quasiparticles with reduced bandwidth is clearly seen. At high energies and far away from the Fermi surface the spectra acquire an additional peak that describes excitations in the Hubbard band. The dispersion in Hubbard bands is weaker along the \ensuremath{\Gamma}-Z, than \ensuremath{\Gamma}-X or X-Z direction. The density of states of a correlated system, as given by the perturbation theory, remains logarithmically singular but the singular weight is reduced with respect to the uncorrelated one. In addition, the correlations transfer the spectral weight out of the low-energy region, where only a narrow Kondo-like structure seems to remain. The spectral properties of the 2D Hubbard model obtained by the truncated perturbation expansion resemble in many ways the recent experimental data on metallic cuprates.
We have studied the pseudogap formation in the single-particle spectra of the half-filling two-dimensional Hubbard model. Using a Green's function with the one-loop self-energy correction of the spin and charge fluctuations, we have numerically calculated the self-energy, the spectral function, and the density of states in the weak-coupling regime at finite temperature. Pseudogap formations have been observed in both the density of states and the spectral function at the Fermi level. The pseudogap in the spectral function is explained by the non-Fermi-liquid-like nature of the self-energy. The anomalous behavior in the self-energy is caused by both the strong antiferromagnetic spin fluctuation and the nesting condition on the non-interacting Fermi surface. In the present approximation, we find a logarithmic singularity in the integrand of the imaginary part of the self-energy. Concerning the energy dependence of the spectral function and the self-energy, two theorems are proved. They give a necessary condition in the self-energy to produce the pseudogap at the Fermi level. The pseudogap in the spectral function is highly momentum dependent on the Fermi surface. It opens initially in the (±π,0)(\pm π,0)(±π,0), (0,±π)(0,\pm π)(0,±π) regions as the normal state pseudogap observed in the high-TcT_cTc​ superconductors and if the interaction is increased, it spreads to other Fermi surface sectors. The anisotropy of the pseudogap is produced by the low-energy enhancement of the spin excitation around Q=(π,π){\bf Q}=(π,π)Q=(π,π) and the flatness of the band dispersion around the saddle point.
We examine the quasiparticle lifetime and spectral weight near the Fermi surface in the two-dimensional Hubbard model. We use the FLEX approximation to self-consistently generate the Matsubara Green's functions and then we analytically continue to the real axis to obtain the quasiparticle spectral functions. We compare the spectral functions found in the nearest neighbor hopping only Hubbard model with those found when second neighbor hopping is included. This separates the effects of nesting, the Van Hove singularity and the short-ranged antiferromagnetic correlations. The quasiparticle scattering rate is enhanced along the (0,pi) to (pi,pi) Brillouin zone diagonal. When the density is close to half-filling these 'hot-spots' lie on the Fermi surface and the scattering rate increases with decreasing temperature. For the next-nearest neighbor hopping scenario we observe a large range of doping where there is no antiferromagnetism but the scattering rate has a linear temperature dependence. On decreasing the interaction this non-Fermi liquid behavior is confined to doping levels where the Fermi energy lies near to the Van Hove singularity. We conclude that the 'hot-spots' are associated with the antiferromagnetic phase transition while the linear temperature dependence of the scattering rate is associated with the Van Hove singularity.
Single-particle excitation spectra of the two-dimensional Hubbard model on the square lattice near half filling and at zero temperature are investigated on the basis of the self-consistent projection operator method. The method guarantees a high accuracy of the spectra with high energy and high momentum resolutions. It takes into account long-range intersite correlations as well as the strong on-site correlations. Effects of nonlocal excitations are clarified by comparing the results with those of the single-site approximation. The calculated spectra verify the quantum Monte-Carlo results for finite temperatures. The spectra at the Fermi level yield a hole-like Fermi surface in the underdoped region and an electron-like Fermi surface in the overdoped region. From a numerical analysis of the momentum dependent effective mass and self-energy, it is concluded that a marginal Fermi-liquid like state persists even at finite doping concentrations in the strongly correlated region because a van Hove singularity is pinned to the Fermi surface. It is also found that a kink structure appears in the quasiparticle energy band in the same region. The kink is shown to be caused by a mixing between the quasiparticle band and an excitation band with strong short-range antiferromagnetic correlations. These results suggest an explanation for some of the unusual properties of the normal state in high-TcT_{\rm c}Tc​ cuprates.
The single-particle spectral properties near the Mott transition in the two-dimensional Hubbard model with next-nearest-neighbor hopping are investigated by using cluster perturbation theory. Complicated spectral features of this model are simply interpreted, by considering how the next-nearest-neighbor hopping shifts the spectral weights of the two-dimensional Hubbard model. Various anomalous features observed in hole-doped and electron-doped cuprate high-temperature superconductors are explained in a unified manner as properties near the Mott transition in a two-dimensional system whose spectral weights are shifted by next-nearest-neighbor hopping.